Academic Journal
Wavelet regression in random design with heteroscedastic dependent errors
| العنوان: | Wavelet regression in random design with heteroscedastic dependent errors |
|---|---|
| المؤلفون: | Rafa̷l Kulik, Marc Raimondo |
| المساهمون: | The Pennsylvania State University CiteSeerX Archives |
| المصدر: | http://arxiv.org/pdf/0909.0384v1.pdf. |
| سنة النشر: | 2009 |
| المجموعة: | CiteSeerX |
| الوصف: | We investigate function estimation in nonparametric regression models with random design and heteroscedastic correlated noise. Adaptive properties of warped wavelet nonlinear approximations are studied over a wide range of Besov scales, f ∈ B s π,r, and for a variety of L p error measures. We consider error distributions with Long-Range-Dependence parameter α,0 < α ≤ 1; heteroscedasticity is modeled with a design dependent function σ. We prescribe a tuning paradigm, under which warped wavelet estimation achieves partial or full adaptivity results with the rates that are shown to be the minimax rates of convergence. For p> 2, it is seen that there are three rate phases, namely the dense, sparse and long range dependence phase, depending on the relative values of s,p,π and α. Furthermore, we show that long range dependence does not come into play for shape estimation f − ∫ f. The theory is illustrated with some numerical examples. 1. Introduction. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| Relation: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.246.4052; http://arxiv.org/pdf/0909.0384v1.pdf |
| الاتاحة: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.246.4052 http://arxiv.org/pdf/0909.0384v1.pdf |
| Rights: | Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
| رقم الانضمام: | edsbas.D36C2AAB |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |